The reality of having to take a required writing class or even a one-on-one writing tutorial can instill fear in even the most successful of students. Writing is for so many a very intimidating activity; it is no wonder that students who have more difficulty reading and writing than their peers are simply resistant to the idea that they will ever become "good" writers.
Although students with LDs have been listening to and speaking English for almost as long as you have, their different learning styles have prevented them from being able to apply the "templates" these experiences provide for more standard learners. Often, they are not aware of the mistakes they are making, and cannot understand why they are being misunderstood.
They have been called lazy, dumb, and unmotivated, and they are probably frustrated, anxious, and insecure. They often rely on the things they are good at and repel those activities they are not (which tend to be just the sort of things we assign in composition classes). Often these students did all right in high school, but are suddenly having difficulty in college.
What does all of this point to? The reality is that these students will have to work harder than students with traditional learning styles; they have to be more mature college students, more organized, more focused, more self-motivated, more ambitious, and more consistent. If they fall prey to the temptations other students are allowed, they are much more likely to fall behind and drop out of college. It will also take them more time to complete assignments, and they will have to make that time during schedules equally as busy as their classmates.' Again, you can try to inspire this kind of enthusiasm, but you cannot provide it.
If you have pointed out the available resources on our campus, have done your best to accommodate the student in your class or tutorial, and have provided the strategies you think might help, it is up to the student to get formal assessment and to make use of the other resources available.